Problem: Einsteinium- $253$ is an element that loses about $\dfrac23$ of its mass every month. A sample of Einsteinium- $253$ has $450$ grams. Write a function that gives the sample's mass in grams, $S(t)$, $t$ months from today. $S(t)=$
Solution: If the sample loses $\dfrac{2}{3}$ of its mass each month, that means $\dfrac{1}{3}$ of the mass remains each month. So each month, the sample's mass is multiplied by a factor of $\dfrac{1}{3}$. If we start with the initial mass, $450$ grams, and keep multiplying by $\dfrac{1}{3}$, this function gives us the sample's mass $t$ months from now: $S(t)=450\left(\dfrac{1}{3}\right)^t$